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50                                 CHEMICAL ENGINEERING
of joints and decrease the cost of installation. They should be used liberally. Ample use of special fittings, where joints may thereby be saved, is also good practice. Drainage is of prime importance. Pipes approximately horizontal should slope downward in the direction of steam flow and should be drained at low points. Branches should be taken from tops or sides of pipes supplying them. High-level high-pressure drips may be returned directly to the boiler. Clean drips from other points may enter an open feed heater or hot well. Greasy low-pressure drips are usually wasted.
Units and Definitions.—Units of voltage, current, resistance and power are the volt (F), ampere (I), ohm (r) and watt (P). For direct current, I = V/r, p = VI. 1 hp. = 746 watts. 1 kilowatt (kw.) = 1.34 hp. = 1,000 watts. The heating effect is Pj> = rl2. In alternating currents, the voltage and current are out of phase because of inductance, and both vary continuously during each revolution of the generator. If the variation may be expressed as a sine curve against time (which is approximated in usual practice), P = VI cos 6 where 6 is the angular phase difference and_cos 6 is the power factor. The effective voltage or current is the maximum -f- '2. An alternating-current generator may send out a series of alternating currents of different phase over different conductors. The angle between these different phases remains constant. The so-called single-phase system is a two-phase arrangement with one terminal of each winding connected to a common j unction point (neutral point) while the other terminals of the windings feed the live wires. A similar three-phase winding constitutes the Y arrangement: whereas the A arrangement connects all windings in series with line wires brought out from the junctions. If Ii, Vi denote line current and voltage, n = number of windings, the following relations hold:
A                               Y
Phase current..............          Ii/2 sin -                         Ii
Phase voltage..............           Vp = Vl              Vp = Vt/2 sin ~
Voltage to neutral........ ..          Vp/2 sin -                        Vp
Volt-amperes..............        nVJi/2 sin -             nVJi/2 sin -
n                            n
A period (alternating current) is the time required for an alternating current or voltage to complete a cycle of values. Frequency = periods per second.
Series arrangements are end-to-end: current passing from one device to another in succession. Multiple or pamper arrangement exists where devices (lamps, for example) are connected across mains, each lamp being independent of all others.
The circular mil is the area of a circle of Mooo in. diameter. Torque, T, is tangential pull at 1 ft. radius, in pounds. If R = revolutions per second, the corresponding horsepower is 7rT#/550.
Systems.—Direct current is used for short distances of transmission and low voltages, or where speed variation is necessary. In most industrial applications direct current gives higher power efficiency but reduced ruggedness and reliability.